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Unformatted text preview: Ge/Ay133 Jovian planet formation. Coreaccretion or gravitational instability? The radiusmass relationship and M.o.I. are used to infer the presence of primordial cores of 1030 M earth . Properties of the Jovian Planets in the Solar System P ∝ ρ 2 for H 2He I/MR 2 =0.4 for a uniform sphere I/MR 2 =0.26 for P ∝ ρ 2 1113 Saumon & Guillot 2004 core mass constraints based on EOS [preferred EOS] [envelope] Caveat! Core mass estimate based on high pressure EOS: OK for Saturn, but… Saumon & Guillot (2004) core mass constraints based on EOS dubious EOS? Previously favored. Currently preferred EOS (Boriskov et al. 2005) [envelope] …very large extrapolations & uncertainties for Jupiter! (need better high P,T measurements, very difficult) Theory of nucleated instability: Cores in Jovian planets are almost certainly primordial, and the fact that all such objects in the solar system radiate more energy than they receive means they started hot. This has led to the development of the coreaccretion model in which gas accretes onto cores built along the lines discussed in Lec. #12. Hill Sphere Photosphere Dense core Adiabatic envelope Ambient solar nebula ~Isothermal r H Theory of nucleated instability: How do we analyze this situation? The extent of the envelope is determined via hydrostatic equilibrium. Key is the temperature profile, which is established by the radiative transfer equations below. L is the luminosity, K is the mass opacity coefficient. Hill Sphere Photosphere Dense core Adiabatic envelope Ambient solar nebula r H The minimum luminosity that needs to be radiated is that which balances any ongoing accretion (equation at left). From this the mass/density properties of the envelope can be estimated: Hill Sphere Photosphere Dense core Adiabatic envelope r H Thus we need to solve for the density structure to get the envelope mass, which means we need to know the temperature profile. Solving the radiative transfer equations yields (for the envelope): Hill Sphere Photosphere Dense core Adiabatic envelope r H Ideal gas Clearly the value of K is critical. Gas can only contribute a small fraction of the overall opacity, and so the dust grain or ice content in the envelope must be known, or assumed... How massive does the core need to be for the atmosphere to collapse? Photosphere Dense core Adiabatic envelope Stevenson 1982, Pl. Sp. Sci. 30 , 755 f~ K in cm 2 /g Setting dM c /dM t =0 gives ( α ∝ μ 4 29 The gas/dust ratio in the envelope is also critical for TIME SCALES!...
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